Methods based on nuclear energy density functional (EDFs) have already become the standard tool in describing nuclear ground states and low-energy excited states [1,2]. In the present contribution, I will focus on recent developments related to the quest for new-generation functionals that might provide us with increased precision of global description of nuclear data and link low-energy phenomena to ab-initio properties of nuclear matter and nuclear interactions. The main line of generalizations will be in expansions of EDFs in series of higher-order corrections related to derivatives of densities and fields [3]. I will also discuss generalizations of momentum-dependent interactions, like the Skyrme force, to higher orders [4] and derivations of quasilocal higher-order functionals from nonlocal ones [5]. Finally, I will present ideas related to introducing new functionals based on regularized zero-range forces [6].
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